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OG2015 DS If n + k = m

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by Jay@ManhattanReview » Sat Sep 16, 2017 3:16 am

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lionsshare wrote:If n + k = m, what is the value of k?

(1) n = 10
(2) m + 10 = n

OA: B

Please, anyone, share the solution to this problem. Thank you.
Statement 1: n = 10

By plugging in the value of n = 10 in the equation n + k = m, we get 10 + k = m. Thus, k = m - 10. But we do not know the value of m, so we cannot get the value of k. Insufficient.

Statement 2: m + 10 = n

=> 10 = n - m; by transposing m to LHS

Since from the given equation n + k = m, we get m - n = k, thus, k = 10. Sufficient.

The correct answer: B

Hope this helps!

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by ceilidh.erickson » Thu Apr 05, 2018 1:30 pm

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lionsshare wrote:If n + k = m, what is the value of k?

(1) n = 10
(2) m + 10 = n

OA: B

Please, anyone, share the solution to this problem. Thank you.
Whenever you're given information about 2 or more variables and asked the value of one of them, rephrase in terms of the others.

Question: k = ?
Given: n + k = m

First, solve for k:
k = m - n
Thus, if we want to know the value of k, our rephrased question is:
what is the value of m - n?

(1) n = 10
Just the value of n alone won't give us the value of m - n. Insufficient.

(2) m + 10 = n
Rearrange:
m - n = -10

This gives us a value for our target question m - n, so this is sufficient.

The answer is B.

It is also worth noting that this question is what I like to call a C-Trap: if we put the 2 statements together, we very obviously get all the values we need, but we didn't do any conceptual work. If you recognize that happening, it's a C-Trap.
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by ceilidh.erickson » Thu Apr 05, 2018 1:33 pm

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For more on C-traps, see:
https://www.beatthegmat.com/og-13-156-t ... tml#766502
https://www.manhattanprep.com/gmat/blog ... fficiency/
https://www.manhattanprep.com/gmat/blog ... ncy-traps/
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Harvard Graduate School of Education
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by Brent@GMATPrepNow » Mon Apr 09, 2018 5:44 am

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lionsshare wrote:If n + k = m, what is the value of k?

(1) n = 10
(2) m + 10 = n
I'd typically use the same approach that Ceilidh used, but here's one more approach...

Target question: What is the value of k?

Given: n + k = m

Statement 1: n = 10
Let's TEST some values
There are several values of m, n and k that satisfy statement 1. Here are two:
Case a: m = 12, n = 10, and k = 2. So, we have 10 + 2 = 12. In this case, k = 2
Case b: m = 13, n = 10, and k = 3. So, we have 10 + 3 = 13. In this case, k = 3
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: m + 10 = n
Take: m + 10 = n
Subtract 10 from both sides to get: m = n - 10
Rewrite as: m = n + (-10)
Rewrite as: n + (-10) = m
Add some color: n + (-10) = m
Compare this to the given information: n + k = m
From this, it is clear that k = -10
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
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by Scott@TargetTestPrep » Sun Jul 22, 2018 5:18 pm

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lionsshare wrote:If n + k = m, what is the value of k?

(1) n = 10
(2) m + 10 = n
We are given that n + k = m, and we need to determine the value of k. Since we know that n + k = m, we know that k = m - n. Thus, if we determine a value for m - n, we will know the value of k.

Statement One Alone:

n = 10

Although we know that n = 10, without knowing the value of m, we cannot determine the value of k. Statement one alone is not sufficient. We can eliminate answer choices A and D.

Statement Two Alone:

m + 10 = n

Manipulating statement two we get:

m + 10 = n

m - n = -10

Since we know that m - n = -10, we know that k = -10. Statement two alone is sufficient.

Answer: B

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by [email protected] » Fri Jul 27, 2018 11:03 am

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Hi All,

We're told that N + K = M. We're asked for the value of K. If you're familiar with 'system math', then the given equation might make you think of a specific Algebra rule: with 3 variables, I would need 3 unique equations to solve for EACH variable. While that rule is true, it's important to remember that the question is NOT asking us to solve for all 3 variables - it's only asking us for the value of K - so we might not need two additional unique equations to properly answer this question.

1) N = 10

Combining the information in Fact 1 with what we already know, we would have...
10 + K = M
With two variables and one equation, K could be ANY value.
Fact 1 is INSUFFICIENT

2) M + 10 = N

We can substitute the value of 'N' in this equation into the initial equation...
N + K = M
(M + 10) + K = M
10 + K = 0
K = -10
Fact 2 is SUFFICIENT

Final Answer: B

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